Representation and Stability of Solutions for Impulsive Discrete Delay Systems with Linear Parts Defined by Non-Permutable Matrices

• Xianghua Jin ^[1] ; JinRong Wang ^[3] ; Dong Shen ^[2]
  1. [1] Guizhou University

     Guizhou University

     China

     
  2. [2] Renmin University of China

     Renmin University of China

     China

     
  3. [3] Guizhou University & Huaqiao University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • In this paper, we introduce a modified delayed perturbation of discrete matrix exponential for impulsive linear discrete delay systems with non-permutable matrices. Using the Z-transform method and its alternative method, we derive a clear representation of the solution, which covers both impulsive and non-impulsive cases in the existing literature. Moreover, using the representation of solution, discrete Gronwall’s inequality, and discrete Bihari’s inequality, we establish several results of exponential stability.

    Numerical examples are given to verify these results.